A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F₁ on a particle placed at a distance 3R from the centre of the sphere. A spherical cavity of radius R/2 is now made in the sphere as shown in the figure. The sphere with cavity now applies a gravitational force F2 on the same particle. The ratio F₂ /F₁ is

Find the distance between centre of gravity and centre of mass of a two particle system attached to the ends of a light rod. Each particle has same mass. Length of the rod is R, where R is the radius of earth

At what height above the earth’s surface does the acceleration due to gravity fall to 1% of its value at the earth’s surface?

Two concentric shells of uniform density of mass M₁ and M₂ are situated as shown in the figure. The forces experienced by a particle of mass m when placed at positions A, B and C respectively are (given OA = p, OB = q and OC = r)

With what angular velocity the earth should spin in order that a body lying at 30° latitude may become weightless [R is radius of earth and g is acceleration due to gravity on the surface of earth]

A man of mass m starts falling towards a planet of mass M and radius R. As he reaches near to the surface, he realizes that he will pass through a small hole in the planet. As he enters the hole, he sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass and a point mass at the center. Change in the force of gravity experienced by the man is

Man outside the shell is 2GMm/3R^2

If the radius of the earth be increased by a factor of 5, by what factor its density be changed to keep the value of g the same?

A spherical hole of radius R/2 is excavated from the asteroid of mass M as shown in fig. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is

A steady flow of water passes along a horizontal tube from a wide section X to the narrower section Y, see figure. Manometers are placed at P and Q at the sections. Which of the statements A, B, C, D, E is most correct?

A cylindrical vessel is filled with a liquid up to height H. A small hole is made in the vessel at a distance y below the liquid surface as shown in figure. The liquid emerging from the hole strike the ground at distance x

A tank is filled upto a height h with a liquid and is placed on a platform of height h from the ground. To get maximum range x_m a small hole is punched at a distance of y from the free surface of the liquid. Then

Figure shows a siphon. Choose the wrong statement

The spring balance A reads 2 kg with a block m suspended from it. A balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in the figure in this situation

The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section A and height h. The upper part is a conical vessel of height h with base area ‘A’ and top area ‘a’ and the walls of the vessel are inclined at an angle 30° with the vertical. A liquid of density r fills both the sections upto a height 2h. Neglecting atmospheric pressure.

A soap bubble has radius R and thickness d (<< R) as shown. It colapses into a spherical drop. The ratio of excess pressure in the drop to the excess pressure inside the bubble is

A liquid is filled in a spherical container of radius R till a height h. At this positions the liquid surface at the edges is also horizontal. The contact angle is